Explain as simple as possible please?: How does the genetic code provide evidence of the common ancestry of all life?

The genetic code is mostly conserved in every organism from bacteria to humans (there are some very small differences). However, there is no rule that says the genetic code must work exactly the way it does. So, if for example different species "appear out of thin air" (as people used to think) then we would expect them to have different genetic codes. In other words, the most plausible way to explain the fact that the genetic code works the same for every organism is that it was passed down from the first common ancestor of all life.

http://www.pbs.org/wgbh/evolution/library/04/4/l_044_02.html
This thread of genetic similarity connects us and the roughly 10 million other species in the modern world to the entire history of life, back to a single common ancestor more than 3.5 billion years ago. And the evolutionary view of a single (and very ancient) origin of life is supported at the deepest level imaginable: the very nature of the DNA code in which the instructions of genes and chromosomes are written. In all living organisms, the instructions for reproducing and operating the individual is encoded in a chemical language with four letters -- A, C, T, and G, the initials of four chemicals. Combinations of three of these letters specify each of the amino acids that the cell uses in building proteins.